I was reading SEP article on types and tokens, and got interested in the concept of 'occurrence'. We would describe the fact that the number '2' appears multiple times in an expression as an example of 'occurrences' of a number, so a concept can be 're-used' and occur multiple times.

But is this just a property of 'abstract' objects or ideas? Is it more common for them? Can concrete objects/people also have multiple 'occurrences'?

In the article they use the idea of a person appearing twice in a lottery, this is a strange idea, but perhaps the person 'occurring' is more of a reference than anything.

  • 1
    Section 5 of the same article describes the relations between types and tokens. One theory is that types are universals (abstract objects), that cannot be concrete, and tokens are their concrete instances. Another theory is that types are sets/classes, and tokens are their elements, in which case there isn't much different in concreteness. Types are just sets of all their occurrences. Parsons distinguishes "quasi-concrete" (letters, shapes) and "pure abstract" (numbers) types, the former are close to concrete but can have instances, see Jeshion.
    – Conifold
    Aug 24, 2022 at 8:47
  • 1
    If a "concrete object" is an individual, it has no multiple occurrences: two stones are different objects and two humans are different individuals. The distinction applies to "abstract" like symbols: if we assume that there is "the" number three, we have to face the fact that from one side we manage it as an individual (why call it "the"... otherwise) but at the same time we "use" it many times. Aug 24, 2022 at 10:49
  • 1
    See your previous post: a concrete object "disappear" after "using" it, while an abstract does not. Aug 24, 2022 at 12:09
  • 1
    If the number 2 occurs twice in "two apples and two oranges" then whoever John is occurs twice in "John always puts John first". It's not restricted to abstract objects. Aug 24, 2022 at 14:13
  • 1
    Type/token/occurrence could be extremely tricky especially when dealing with structural types which may have multiple occurrences of simpler universals within. Lewis proposed there're only 2 possible types of structural types (ersatz vs heap) while Wetzel argued there's another "occurrence" view of the heap or its constitutive simpler type similar to your examples, which Lewis denied. See Wetzel, Linda (1993), “What Are Occurrences of Expressions?” Journal of Philosophical Logic, 22: 215-220... Aug 24, 2022 at 20:28

2 Answers 2


There is nothing unusual about abstract objects in this sense. Consider the sentence "John always puts John first." In this sentence, "John" is a word, not to be confused with John who is a person. It's easy to tell the difference: The word "John" has four four letters and is a noun. The person John has no letters; he has a brain and a liver and other organs. He isn't a noun; he's a man.

Just because John can appear twice in the same sentence, that doesn't mean that he can be duplicated. It only means that he can be referred to multiple times.

Now consider the sentence "Ten is the product of ten and one." In this sentence, "ten" is a word, not to be confused with the number ten. It's easy to tell the difference: the word "ten" has three letters and is a noun. The number ten has no letters, but it does have factors. It is not a noun; it is an even number.

The situation is exactly the same in both cases. The sentence contains multiple references to a single thing, so it has multiple occurrences of that thing. Occurrences are a purely linguistic thing in this case, they have nothing to do with what kind of thing is being referred to.

  • 2
    +1) Sounds like you're on the right track since your proposition "Occurrences are a purely linguistic thing in this case" is similar in spirit with what Lewis called "ersatz structural type". However, your use of John and Ten are clearly referring to your intended referent, either being a concrete person or an abstract number, respectively, in your intended everyday language domain. In the manner you mention "John has four letters and is a noun" such "John" clearly is not denoting any term in your intended everyday language domain... Aug 25, 2022 at 5:45


Look at yourself at the mirror, twice. The second time, every possible part of you has changed in you: your atoms, your energy states, your mind, etc.

The second time you look yourself at the mirror, you are looking at a second instance of you, which is clearly, overwhelmingly different from that of the first look (same happens with any other entity, rocks, houses, rainbows, etc.). There is the answer: strictly, concrete objects never exist as a single physical instance, change is permanent. While a concrete object seems static, it is never the same.

Where's the issue here?

In thermodynamics, there's a contrast in perceptions: microstatically, all systems change permanently (e.g. internal particles exchange energy constantly), while macrostatically, things seem static (constant temperature of a body is possible). Even ideas are subject to such principle (not in thermodynamics, evidently): two different thoughts have different parts. However, they can refer to the same concept.

So, the problem is not the possibility of multiple instances of concrete objects, but unique instances of abstract objects: how are immutable concepts / types possible? How is mathematics possible? That should be the question. No answer here, but the Kant's Transcendental Aesthetics section of his Critique of Pure Reason provides some insights worth considering.

Technical remark: an abstract object requires of two perceptions (two different instants of time) to be compared and found to be the same.

  • 1
    In your mirror example since every concrete atom/energy state of you changes between your two consecutive looks, their occurrences then is not multiple. And the seemingly constant "you" is better classified as abstract universal since it's not the simple aggregated heap from all those constantly changed concrete atoms/energy states which must be also constantly changing... Aug 25, 2022 at 3:48
  • @DoubleKnot You are telling that your physical body is an "abstract universal"...
    – RodolfoAP
    Aug 25, 2022 at 3:55
  • 2
    As I described above your physical body could be straightforwardly conceived as an aggregate of your admitted constantly changing atoms/energy states thus per mereology your physical body as a heap is concrete and also constantly changing accordingly in this sense (in another sense you could treat your atoms and body as simpler and heap types, respectively, that's why it could become tricky easily even from such a seemingly simple example). But clearly you described "you" as commonly understood "self" is subtly another thing, if it exists at all per the famous Anatta doctrine... Aug 25, 2022 at 4:05
  • 2
    Also you haven't addressed "since every concrete atom/energy state of you changes between your two consecutive looks, their occurrences then is not multiple." Aug 25, 2022 at 4:11

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .